It depends. The truth is, most professional designers do not have a writing component as part of their everyday job. Writing can be useful when it comes to case study documentation, presentation preparation, or for communicating a studio philosophy. Writing is one area of graphic design education that I feel is lacking. While my students may not always agree, the fact that I ask each student to write a single-page paper prior to designing a project, has helped to focus their intent, enable them to think conceptually broad and to carefully consider stylistic choices. The writing process also helps in other
ways; presentations are better because students have a stronger understanding of their own work; it gives the professor and student something tangible to discuss; it sets a workable timeline; and it eliminates a lot of wasted time due to an unclear focus.

From a fine art standpoint, writing tends to take away some mystery from the work, but it can also add a level of understanding unattainable by viewing the work on its own. I’m paraphrasing, but in the book Writing for the Visual Arts (Mashey Bernstein & George Yatchisin), the authors make the point that as an artist, you can write about your own work and dictate the manner in which people view and discuss it; or
you can choose to not write about it, at which point your work will be discussed in a manner that others interpret it — depending on your philosophy, this may or may not be a desirable outcome.